91Ó°ÊÓ

Use a graphing utility to graph each pair of functions in the same viewing rectangle. Use a viewing rectangle that shows the graphs for at least two periods. $$y=4 \cos \left(2 x-\frac{\pi}{6}\right) \text { and } y=4 \sec \left(2 x-\frac{\pi}{6}\right)$$

Why are the trigonometric functions sometimes called circular functions?

The average monthly temperature, \(y,\) in degrees Fahrenheit, for Juneau, Alaska, can be modeled by \(y=16 \sin \left(\frac{\pi}{6} x-\frac{2 \pi}{3}\right)+40,\) where \(x\) is the month of the year (January \(=1,\) February \(=2, \ldots\) December \(=12\) ). Graph the function for \(1 \leq x \leq 12 .\) What is the highest average monthly temperature? In which month does this occur?

Use a graphing utility to graph each pair of functions in the same viewing rectangle. Use a viewing rectangle that shows the graphs for at least two periods. $$y=-3.5 \cos \left(\pi x-\frac{\pi}{6}\right) \text { and } y=-3.5 \sec \left(\pi x-\frac{\pi}{6}\right)$$

In Exercises \(61-86,\) use reference angles to find the exact value of each expression. Do not use a calculator. $$\sin \left(-\frac{35 \pi}{6}\right)$$

In Exercises \(85-92,\) determine the domain and the range of each function. $$f(x)=\cos \left(\cos ^{-1} x\right)$$

Find the absolute value of the radian measure of the angle that the second hand of a clock moves through in the given time. 4 minutes and 25 seconds

Define the sine of \(t\).

In Exercises \(87-92\), find the exact value of each expression. Write the answer as a single fraction. Do not use a calculator. $$\sin \frac{\pi}{3} \cos \pi-\cos \frac{\pi}{3} \sin \frac{3 \pi}{2}$$

In Exercises \(85-92,\) determine the domain and the range of each function. $$f(x)=\cos ^{-1}(\cos x)$$